Question: $h(t) = -3t-2$ $g(t) = t+4+3(h(t))$ $ h(g(-4)) = {?} $
First, let's solve for the value of the inner function, $g(-4)$ . Then we'll know what to plug into the outer function. $g(-4) = -4+4+3(h(-4))$ To solve for the value of $g$ , we need to solve for the value of $h(-4)$ $h(-4) = (-3)(-4)-2$ $h(-4) = 10$ That means $g(-4) = -4+4+(3)(10)$ $g(-4) = 30$ Now we know that $g(-4) = 30$ . Let's solve for $h(g(-4))$ , which is $h(30)$ $h(30) = (-3)(30)-2$ $h(30) = -92$